Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-3y &= 3 \\ 9x+3y &= -4\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -9x-4$ Divide both sides by $3$ to isolate $y$ $y = {-3x - \dfrac{4}{3}}$ Substitute this expression for $y$ in the first equation. $-8x-3({-3x - \dfrac{4}{3}}) = 3$ $-8x + 9x + 4 = 3$ Simplify by combining terms, then solve for $x$ $1x + 4 = 3$ $1x = -1$ $x = -1$ Substitute $-1$ for $x$ back into the top equation. $-8( -1)-3y = 3$ $8-3y = 3$ $-3y = -5$ $y = \dfrac{5}{3}$ The solution is $\enspace x = -1, \enspace y = \dfrac{5}{3}$.